The only issue I have with it is that it's a pretty niche application. I think most sites will have a single database probably in a single location, in which case you don't gain anything from edge compute as far as I can tell.

Maybe if these things came with some kind of fancy "edge database" it would cover normal use cases, but they never seem to mention that so I assume it doesn't exist.

Single-instance private FaaS (as opposed to multi-instance public FaaS) allow to implement edge databases, assuming there is persistence. Currently only Cloudflare offers this with Durable Objects and the industry seems to not have caught on, maybe not even understood, yet.